Pendula

I think we did that one to death here Noel :-

**LINK**

although just now I can't remember what our conclusions were

regards Martin

Foucault

[ no pun intended ]

MichaelG.

Edited By Michael Gilligan on 20/11/2022 14:35:20

There's an interesting point here about the influence of the atmosphere on a pendulum's rate. It has 3 effects.

One is that the bob has a buoyancy, which reduces it's effective weight though not its mass - or in effect the value of G is reduced. This makes the pendulum go slower with increasing pressure.

Secondly, the bob brings along with it a slug of air in the boundary layer. This in effect increases its mass, but not its weight because it isn't attached. As the pressure increases so does the density so the added mass increases. This effect is sometimes called "accession to inertia" and also makes the pendulum go slower with increasing pressure. For most bob shapes the amount is about equal to the buoyancy effect, and the fractional sensitivity of the rate to pressure variation ends up being the fractional variation in air pressure divided by the ratio of the bob density to air density. Dense bob materials like iron, lead and tungsten are therefore preferred.

Third, increasing pressure increases drag and reduces amplitude, which speeds up the pendulum through reduced circular deviation. Actually it turns out there's an amplitude where these three effects cancel out and the pendulum can be made insensitive to pressure variation.

Hi MichaelG, I have download that from your link, but haven't gotten round to reading any of it yet but should find time in due course.

Regards Nick.

Hi as MichaelG has mentioned, Foucault, I took this photo below of the one that was in the Science Museum in London ten years ago.

I was hoping to see a really large one back in 2013 in Paris, which I think was in a cathedral, but it had been taken out due to renovations that were going to take three years, and I haven't been to Paris since then.

Regards Nick.

Edited By Nicholas Farr on 20/11/2022 16:11:52

I don't know if it's the same one Nick, but there is a very impressive one in the Musee des Arts et Metiers which I visited 3 years ago. The Paris equivalent of the Science Museum, and very much worth a visit. Allow an afternoon at least.

Clocks are typically mounted in a fixed orientation, so the Foucault effect might cause a clock bob to swing more easily when the earth is aligned with the spring's flat side, because the movement otherwise tends to twist the spring as the planet rotates under the suspension point.

Does the earth's rotation disturb a clock pendulum rigidly suspended with a flat spring? Or is the effect too small to matter on a clock sized pendulum, because the elliptical path is almost a straight line? I notice Foucault pendulums consist of a large heavy bob suspended on a long thin line, so perhaps a cathedral sized enclosure and a massive pendulum is needed to show the apparent movement?

The maths doesn't seem impossible: if 10kg bob is swinging 5 degrees on the end of a 20 metre rod, and the support beam is exactly North South, how much torque is applied to the suspension by the earth's rotation each hour?

Dave

Dave

You might be interested to read this: **LINK**

https://britastro.org/wp-content/plugins/baa-frontend-tweaks/baa-check-file.php?filename=2016/09/JBAA-124-4-Bate.pdf

I assisted Andrew with a couple of his trials, and can confirm that the effect is readily discernible at the pendulum-length that can be configured in a typical parish church.

MichaelG.

Edited By Michael Gilligan on 20/11/2022 20:21:19

http://leapsecond.com/hsn2006/

**LINK**

This Web page links to a set of articles by Tom van Baak that gives a good discussion of tidal effects of the sun and moon on pendulum rate. I think this subsumes Foucault effects too. Particularly interesting is the article on the Fedchenko clock that shows that it's errors over a given month were essentially only caused by gravity variations. The whole site is well worth exploring, especially the articles on testing General Relativity on a family camping trip.

Hi John, thanks for your link, i can't remember if I knew about that one, or if that was undergoing some refurbishment at the time, but the one we were going to see is in the Paris Panthéon and is a copy of the original, which is in the Musée des Arts et Métiers, however, we didn't have any time to change our plan of the places we would visit, as we only did our tour on foot in the few days we were there. I don't know when, if ever, that I'll be going to Paris again, but I can keep both places in mind if I do.

Regards Nick.

No doubt you wrote in jest but I have just noticed that Britten's Guide says "pendulums".

Thanks ega, it was only partly in jest because I know how engineers like correct terminology!

David

Though described as 'archaic' pendula is given as a plural in my Shorter OED. It's allowed!

More power to David's elbow. As everyone should post an obsolete technical spelling every day, I shall refer to Paraffine from now on!

Dave

My understanding is that once a Latin word has been adopted into English then English grammar norms apply, so we have pendulums. People who want to show off their classical education use Latin plurals as in stadia. This doesn't work all the time you don't have alumnuses. Who said English was easy.

What happens when the plural is adopted at the same time. Stadia should remain when talking of distance surely.

Maybe alumniis are alumnii raised to the second power sort of allumnii squared.

;o)

keep 'em coming, Martin

Omnibus / Omnibii?

Latin was taught at my school, but I didn't do it...

Rob

Trouble is omnibus doesn't mean omnibus in Latin.

. . . . as in Ceasar sic in omnibus Brutus sic in hat

:O)

I have just come across this post and thought I would add an experience I had with Big Ben a long time ago. In the summer of 1957 I was visiting Westminster Abbey with my girl friend and got mixed in with a viisting group from a Horological Society. Their next place for them to see was Big Ben and as 3 members of their group had not turned up, invited us both to join them. When we were up the top, being lectured by the guide, he made a big point about the pennies on the pendulam being used to adjust for time. If my memory is correct ,there were 4 of them, just laying on the top about 12 inches from the edge. This information caused raised eybrows and some smiles among the group and afterwards they were unaminmous in saying that it was a good story, but total rubbish and was probably thought up by a previous guide, years before,to impress the tourists. I can remember being impressed with how crude the works were.being more Blacksmith than precision Engineering. The pedulam looked like a raw casting with a couple of lumps of iron bolted to the top, presumably to add to the weight. We were up ther when it struck 2 oclock. we were advised to put our hands over our ears, but I had toohache for the rest of the day!

The stadion (ancient Greek) or stadium (ancient roman) is clearly not an imperial measure and so cannot be discussed on this forum without inviting a choleric response. It was anglicised as the stade, but at 606.9 ft I don't think it is all that useful unless your sat nav speaks Latin.

Nice one Duncan although if Imperial Rome use it it must surely be an “Imperial “ measure.

Martin